A BB&amp;R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

Sewell, Edward C.; Sauppe, Jason J.; Morrison, David R.; Jacobson, Sheldon H.; Kao, Gio K.

doi:10.1007/s10898-011-9793-z

Cited by 18 publications

(11 citation statements)

References 27 publications

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“…The BB&R algorithm has also been effectively applied to other scheduling problems, including the total tardiness scheduling problem, 1|r i | t i [12] and the single machine scheduling problem with sequence dependent setup times, where the objective is to find a schedule with minimum total tardiness, 1|ST sd | t i [29]. There are also practical military applications of the 1|r i | U i scheduling problem that involve limited, highly valued assets that process certain tasks within a given time window (e.g., a surveillance satellite that must photograph as many locations as possible within its overpass time window.)…”

Section: Resultsmentioning

confidence: 99%

New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem

et al. 2010

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The paper proposes a new exact approach, based on a Branch, Bound, and Remember (BB&R) algorithm that uses the Cyclic Best First Search (CBFS) strategy, for the 1|r i | U i scheduling problem, a single machine scheduling problem, where the objective is to find a schedule with the minimum number of tardy jobs. The search space is reduced using new and improved dominance properties and tighter upper bounds, based on a new dynamic programming algorithm. Computational results establish the effectiveness of the BB&R algorithm with CBFS for a broad spectrum of problem instances. In particular, this algorithm was able to solve all problems instances, up to 300 jobs, while existing best known algorithms only solve problems instances up to 200 jobs. Furthermore, the BB&R algorithm with CBFS runs one to two orders of magnitude faster than the current best known algorithm on comparable instances.

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Section: Resultsmentioning

confidence: 99%

New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem

et al. 2010

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“…Kao et al (2009Kao et al ( , 2011 and Sewell et al (2009) demonstrate its effectiveness on a variety of single-machine scheduling problems. Hall et al (2008) also use branch, bound, and remember on a vaccine formulary design problem.…”

Section: Discussionmentioning

confidence: 99%

“…The cyclic best-first search (CBFS) is a new search strategy (Kao et al , 2011Sewell et al 2009) that is a hybrid between DFS and BFS (note that CBFS was formerly called distributed best-first search in Kao et al 2009). CBFS begins by choosing the best subproblem at depth 1.…”

Section: Search Strategymentioning

confidence: 99%

A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

Sewell

Jacobson

2012

INFORMS Journal on Computing

104

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W e present a new exact algorithm for the assembly line balancing problem. The algorithm finds and verifies the optimal solution for every problem in the combined benchmarks of Hoffmann, Talbot, and Scholl in less than one-half second per problem, on average, including one problem that has remained open for over 10 years. The previous best-known algorithm is able to solve 257 of the 269 benchmarks. The new algorithm is based on a branch-and-bound method that uses memory to eliminate redundant subproblems.

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“…Similar approaches that exploit local improvement strategies were introduced by Luo and C. Chu (2007) for the maximum tardiness problem, Sourd (2005) for the earliness-tardiness problem, and by Luo et al (2005) and Luo and Chu (2006). The branch and bound approach presented by Sewell et al (2012) maintains a set of non-dominated solutions during the exploration of the search tree, and uses the set to establish dominance relationships for the current branch.…”

Section: Introductionmentioning

confidence: 99%

Pruning Rules for Optimal Runway Sequencing

Maere¹,

Atkin²,

Burke³

2018

Transportation Science

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This paper investigates runway sequencing for real world scenarios at one of the world's busiest airports, London Heathrow. Several pruning principles are introduced that enable significant reductions of the problem's average complexity, without compromising the optimality of the resulting sequences, nor compromising the modelling of important real world constraints and objectives. The pruning principles are generic and can be applied in a variety of heuristic, meta-heuristic or exact algorithms. They could also be applied to different runway configurations, as well as to different variants of the machine scheduling problem with sequence dependent setup times, the generic variant of the runway sequencing problem in this paper. They have been integrated into a dynamic program for runway sequencing, which has been shown to be able to generate optimal sequences for large scale problems at an extremely low computational cost, whilst considering complex non-linear and non-convex objective functions that offer significant flexibility to model real world preferences and real world constraints. The results shown here counter the proliferation of papers that claim that runway sequencing problems are too complex to solve exactly and therefore attempt to solve them heuristically.

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A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

Cited by 18 publications

References 27 publications

New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem

New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem

A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

Pruning Rules for Optimal Runway Sequencing

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